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%% countabilitySeperation.tex
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%% Made by Alex Nelson
%% Login   <alex@tomato>
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%% Started on  Tue Jun  2 18:57:25 2009 Alex Nelson
%% Last update Tue Jun  2 18:57:25 2009 Alex Nelson
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\begin{defn}\label{defn:firstCountable}
A space $X$ is said to have a \define{countable basis at $x$} if
there is a countable collection $\mathscr{B}$ of neighborghoods
of $x$ such that each neighborhood of $x$ contains at least one
of the elements of $\mathscr{B}$. A space that has a countable
basis at each of its points is said to satisfy the \define{first
  countability axioms} (or just is \define{first countable}).
\end{defn}


